Background

This document has nls (non-linear least squares) regression fits using the LOG-NORMAL functional form to USFS FIA (United States Forest Service Forest Inventory & Analysis) Biomass growth vs. stand biomass relationships. We calculated the biomass of each FIA plot by summing alive tree biomass (as reported by FIA). Stand age is also reported by FIA, using tree-core age estimates from two trees from the dominant size class of the FIA plot.

We considered the following Log-Normal functional form \(B = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left(StdAge /c \right)} {d} \right]} ^2 \right)\), where \(B\) is the plot biomass, \(StdAge\) is the stand age at time of biomass measurement, \(\Delta PDSI\) is the difference in the 9-month annual average PDSI (excluding the winter months, i.e., January-September) over the FIA plot biomass interval, which is defined as the measurement time minus 10 years and a 30-year climate normal from 1960 to 1989, and \(yr\) is the measurement year. Free parameters are: \(ge\): biomass growth enhancement over time, \(\phi\): the effect of climate dryness on stand biomass, \(a\): the y-intercept of the curve, \(a +b\): the peak value of \(B\), \(c\): the \(StdAge\) value at peak \(B\), and \(d\): the log-normal curve shape parameter.

Model selection is used to determine the best fitting models, which is implemented in two parts. The first part selected the best model form using the base model (i.e., excluding phi), and \(\phi\): the effect of changing climate (quantified as \(\Delta PDSI\), or the difference in the Palmer drought severity index from June - August for the 10 years preceding the biomass measurement and the 1960-1989 period).

model 1: simple model \(B = (1 + (yr-1990) \cdot ge/100) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left(B_{t1} /c \right)} {d} \right]} ^2 \right)\)

model 2: phi model \(B = (1 + (yr-1990) \cdot ge/100) \times (1 + \phi \cdot \Delta PDSI) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left(B_{t1} /c \right)} {d} \right]} ^2 \right)\)

Note:

This analysis uses ALL available plot biomass data

which includes the following plot-based filtering criteria:

exclude FIA plots in plantation forests
exclude FIA plots with multiple plot conditions (COND_PROP_UNADJ > 0.95)
exclude FIA plots non-productive stands (i.e., those with less than 20 ft^3/acre/year timber producing capability; SITECLCD of 7)
exclude FIA plots in non-stocked stands (i.e., those with STDSZCD of 5)
exclude FIA plots in non-accessible areas (i.e., private lands etc., COND_STATUS_CD not equal to 1)
exclude FIA plot visits that are not part of the annual inventories (which also includes FIA plot visits for Phase 3 ozone measurements)

Below the model fitting procedure is implemented by ecoprovince:

211 - Northeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   9936     2501.4                                
## 2   9935     2488.4  1 13.012   51.95 6.107e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 107696.3
## 2     2 107646.5

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge   -0.241234   0.106391  -2.267   0.0234 *  
## phi   0.048121   0.006438   7.474 8.41e-14 ***
## a    28.841474   1.209812  23.840  < 2e-16 ***
## b   131.423715   4.344807  30.248  < 2e-16 ***
## c   126.036776   5.371817  23.463  < 2e-16 ***
## d     1.102377   0.040252  27.387  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5005 on 9935 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (2 observations deleted due to missingness)

summary

simple model: fits
phi model: fits

plot residuals

predict and plot

plotting 2

212 - Laurentian Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1  30368      10474                          
## 2  30359      10474  9 0.31831  0.1025 0.9996
##   model      AIC
## 1     1 316275.7
## 2     2 316195.9

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge    0.11401    0.06468   1.763    0.078 .  
## phi   0.00000    0.00308   0.000    1.000    
## a    14.45284    0.39879  36.242   <2e-16 ***
## b    92.71935    1.75123  52.945   <2e-16 ***
## c   128.41078    4.06060  31.624   <2e-16 ***
## d     1.45470    0.02883  50.462   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5874 on 30359 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (30 observations deleted due to missingness)

summary

simple model: fits
phi model: fits

plot residuals

predict and plot

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1  11287     2103.2                           
## 2  11286     2103.2  1 0.009898  0.0531 0.8177
##   model      AIC
## 1     1 123636.4
## 2     2 123638.3

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge   0.01701    0.07494   0.227     0.82    
## a   21.66715    1.50287  14.417   <2e-16 ***
## b  174.62875    6.69913  26.067   <2e-16 ***
## c  154.79638   10.92491  14.169   <2e-16 ***
## d    1.50194    0.05919  25.375   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4317 on 11287 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (2 observations deleted due to missingness)

summary

simple model: fits
phi model: fits
phi-alpha model: does not fit

plot residuals

predict and plot

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1   7907     2576.2                         
## 2   7906     2576.1  1 0.0527  0.1617 0.6876
##   model      AIC
## 1     1 85260.52
## 2     2 85262.36

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge  -0.18074    0.11196  -1.614    0.106    
## a   16.59776    1.14643  14.478   <2e-16 ***
## b  126.23170    4.51869  27.935   <2e-16 ***
## c  116.00466    5.95712  19.473   <2e-16 ***
## d    1.22690    0.04757  25.791   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5708 on 7907 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits

plot residuals

predict and plot

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df      Sum Sq F value Pr(>F)
## 1  13434     2573.5                              
## 2  13433     2573.5  1 -3.4379e-10       0      1
##   model      AIC
## 1     1 140618.9
## 2     2 140620.9

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge  -0.01578    0.06557  -0.241     0.81    
## a   21.63233    1.44962  14.923   <2e-16 ***
## b  109.74919    2.96451  37.021   <2e-16 ***
## c  116.08499    5.44770  21.309   <2e-16 ***
## d    1.44349    0.05263  27.427   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4377 on 13434 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (7 observations deleted due to missingness)

summary

simple model: fits
phi model: fits

plot residuals

predict and plot

plotting 2

231 - Southeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df      Sum Sq F value Pr(>F)
## 1  19930     6319.4                              
## 2  19929     6319.4  1 -9.2132e-10       0      1
##   model    AIC
## 1     1 217248
## 2     2 217250

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge   0.68806    0.07597   9.057   <2e-16 ***
## a   13.36056    0.44646  29.925   <2e-16 ***
## b  144.78186    4.29070  33.743   <2e-16 ***
## c  142.55533    9.68371  14.721   <2e-16 ***
## d    1.87326    0.04721  39.677   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5631 on 19930 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (26 observations deleted due to missingness)

summary

simple model: fits
phi model: fits

plot residuals

predict and plot

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  20856     9549.0                                
## 2  20853     9539.3  3 9.7429  7.0994 9.174e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 232202.4
## 2     2 232164.9

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge  2.320e-01  7.386e-02   3.141  0.00169 ** 
## phi 1.491e-02  5.111e-03   2.917  0.00354 ** 
## a   1.315e+01  5.339e-01  24.639  < 2e-16 ***
## b   1.650e+02  6.700e+00  24.629  < 2e-16 ***
## c   1.800e+02  1.714e+01  10.502  < 2e-16 ***
## d   1.970e+00  6.150e-02  32.036  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6764 on 20853 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (60 observations deleted due to missingness)

summary

simple model: fits
phi model: fits

plot residuals

predict and plot

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)  
## 1   2184     814.28                           
## 2   2183     812.63  1 1.6406  4.4072 0.0359 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 24930.06
## 2     2 24927.64

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge   -0.12750    0.23214  -0.549 0.582893    
## phi   0.03866    0.01855   2.085 0.037219 *  
## a    18.50507    3.93531   4.702 2.73e-06 ***
## b   249.58616   75.54526   3.304 0.000969 ***
## c   306.23891  190.54750   1.607 0.108166    
## d     1.97732    0.35814   5.521 3.77e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6101 on 2183 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.89486, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -18.753, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df      Sum Sq F value Pr(>F)
## 1    240     60.621                              
## 2    239     60.621  1 -3.2081e-11       0      1
##   model      AIC
## 1     1 3071.216
## 2     2 3073.216

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -0.5603     0.4889  -1.146   0.2529    
## a   31.0320    23.7278   1.308   0.1922    
## b  615.5216   155.0120   3.971 9.47e-05 ***
## c  352.7609   165.3432   2.134   0.0339 *  
## d    1.8421     0.3603   5.113 6.50e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5026 on 240 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96457, p-value = 9.228e-06
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.5226, p-value = 0.0004273
## alternative hypothesis: two.sided

predict and plot

plotting 2

251 - Prairie Parkland (Temperate)

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1   2779     735.04                           
## 2   2778     734.99  1 0.053246  0.2013 0.6537
##   model      AIC
## 1     1 29307.39
## 2     2 29309.19

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge  -0.33624    0.15541  -2.164   0.0306 *  
## a   27.65434    2.41852  11.434   <2e-16 ***
## b  103.81353    5.49961  18.877   <2e-16 ***
## c  101.68632    6.64390  15.305   <2e-16 ***
## d    1.11177    0.07391  15.042   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5143 on 2779 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (3 observations deleted due to missingness)

summary

simple model: fits
phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96148, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -24.414, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

255 - Prairie Parkland (Subtropical)

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df    Sum Sq F value Pr(>F)
## 1   1280     483.88                            
## 2   1279     483.88  1 0.0040563  0.0107 0.9175
##   model      AIC
## 1     1 13076.50
## 2     2 13078.49

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -0.5129     0.2501  -2.050   0.0405 *  
## a   14.2442     2.0561   6.928 6.75e-12 ***
## b   83.0909     5.9733  13.910  < 2e-16 ***
## c   69.9975     6.5513  10.685  < 2e-16 ***
## d    1.2098     0.1009  11.991  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6148 on 1280 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (3 observations deleted due to missingness)

summary

simple model: fits
phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.94546, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -12.563, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

261 - California Coastal Chaparral Forest and Shrub

model selection 1

## Error in nls(f_ln_1, data = P_261, start = c(ge = ge.start, a = a.start,  : 
##   Convergence failure: singular convergence (7)
## Error in nls(f_ln_2, data = P_261, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: false convergence (8)
##   model AIC
## 1     1  NA
## 2     2  NA

## Warning in min(AIC1_261$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf

## Error in get(paste("nls_261.", Mod.Sel1, sep = "")) : 
##   object 'nls_261.' not found

summary

simple model: does not fit
phi model: does not fit
unable to fit model (only 64 observations)

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

262 - California Dry Steppe

model selection 1

## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
##   model AIC
## 1     1  NA
## 2     2  NA

## Warning in min(AIC1_262$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf

## Error in get(paste("nls_262.", Mod.Sel1, sep = "")) : 
##   object 'nls_262.' not found

summary

simple model: does not fit
phi model: does not fit
unable to fit model (0 observations)

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df      Sum Sq F value Pr(>F)
## 1    424     97.216                              
## 2    423     97.216  1 -1.4211e-14       0      1
##   model      AIC
## 1     1 5410.454
## 2     2 5412.454

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)  
## ge 2.049e+00  8.421e-01   2.434   0.0154 *
## a  0.000e+00  5.605e+01   0.000   1.0000  
## b  1.000e+03  1.104e+03   0.906   0.3656  
## c  5.000e+03  1.852e+04   0.270   0.7873  
## d  3.487e+00  2.003e+00   1.741   0.0825 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4788 on 424 degrees of freedom
## 
## Algorithm "port", convergence message: both X-convergence and relative convergence (5)
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96675, p-value = 2.737e-08
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -6.1995, p-value = 5.664e-10
## alternative hypothesis: two.sided

predict and plot

plotting 2

313 - Colorado Plateau Semi-Desert

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1    501     172.40                           
## 2    500     172.39  1 0.014962  0.0434 0.8351
##   model      AIC
## 1     1 5435.558
## 2     2 5437.514

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge  -0.78642    0.35499  -2.215   0.0272 *  
## a   25.47377    4.39240   5.800 1.18e-08 ***
## b  110.39796   11.78116   9.371  < 2e-16 ***
## c  131.74298    4.59337  28.681  < 2e-16 ***
## d    0.66796    0.05752  11.613  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5866 on 501 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (2 observations deleted due to missingness)

summary

simple model: fits
phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.9006, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -8.7647, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

315 - Southwest Plateau and Plains Dry Steppe and Shrub

model selection 1

summary

simple model: does not fit
phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

321 - Chihuahuan Semi-Desert

model selection 1

model not fitted (not enough data)

summary

simple model: does not fit
phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## Warning: Removed 1 rows containing missing values (geom_segment).

plotting 2

## Warning: Removed 1 rows containing missing values (geom_segment).

322 - American Semidesert and Desert

model selection 1

summary

simple model: does not fit
phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

Cannot fit model
not enough data (only 3 observations)

331 - Great Plains/Palouse Dry Steppe

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df      Sum Sq F value Pr(>F)
## 1    747     494.66                              
## 2    746     494.66  1 -2.7391e-09       0      1
##   model      AIC
## 1     1 7635.544
## 2     2 7637.544

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -0.3460     0.5299  -0.653 0.513998    
## a   10.0252     2.5769   3.890 0.000109 ***
## b   54.4545     8.0086   6.799 2.15e-11 ***
## c  129.9000    27.9390   4.649 3.94e-06 ***
## d    1.4323     0.2387   6.000 3.08e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8138 on 747 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.86835, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -12.04, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

* Cannot fit model

332 - Great Plains Steppe

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    317     222.58                          
## 2    316     222.33  1 0.25864  0.3676 0.5447
##   model      AIC
## 1     1 3495.858
## 2     2 3497.484

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)
## ge    -0.2643     0.8434  -0.313    0.754
## a     24.2164    15.4301   1.569    0.118
## b    321.7358  2059.4978   0.156    0.876
## c   1383.2317 15422.6995   0.090    0.929
## d      2.3261     4.3085   0.540    0.590
## 
## Residual standard error: 0.8379 on 317 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (2 observations deleted due to missingness)

summary

simple model: fits
phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.85367, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -9.0512, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df     Sum Sq F value Pr(>F)
## 1    141     43.589                             
## 2    140     43.589  1 7.3186e-13       0      1
##   model      AIC
## 1     1 1561.523
## 2     2 1563.523

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge   1.2044     1.3718   0.878 0.381453    
## a   29.3517     8.7951   3.337 0.001082 ** 
## b   67.9425    18.5935   3.654 0.000363 ***
## c  141.8680    14.2903   9.928  < 2e-16 ***
## d    0.6582     0.1398   4.709 5.88e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.556 on 141 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96506, p-value = 0.0008963
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.3833, p-value = 0.0007162
## alternative hypothesis: two.sided

predict and plot

plotting 2

342 - Intermountain Semi-Desert

model selection 1

## Error in nls(f_ln_2, data = P_342, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: singular convergence (7)
##   model      AIC
## 1     1 3420.252
## 2     2       NA

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge   0.3774     1.2278   0.307 0.758792    
## a   16.8483     5.3718   3.136 0.001872 ** 
## b   48.3460    13.2043   3.661 0.000294 ***
## c  120.4151    12.1849   9.882  < 2e-16 ***
## d    0.8567     0.1812   4.729 3.42e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9198 on 314 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: does not fit`

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.88507, p-value = 9.49e-15
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.8708, p-value = 1.112e-06
## alternative hypothesis: two.sided

predict and plot

plotting 2

## Warning: Removed 1 rows containing missing values (geom_point).

## Warning: Removed 1 rows containing missing values (geom_pointrange).

411 - Everglades

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df     Sum Sq F value Pr(>F)
## 1    164     71.662                             
## 2    163     71.662  1 1.5513e-10       0      1
##   model      AIC
## 1     1 1791.752
## 2     2 1793.752

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)  
## ge    -1.3900     0.5698  -2.439   0.0158 *
## a     11.0691    25.2901   0.438   0.6622  
## b    934.1442  6742.0081   0.139   0.8900  
## c   5000.0000 75754.5925   0.066   0.9475  
## d      3.0309     5.3754   0.564   0.5736  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.661 on 164 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96756, p-value = 0.0005489
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.3815, p-value = 7.387e-08
## alternative hypothesis: two.sided

predict and plot

plotting 2

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  10055     1976.7                                
## 2  10054     1970.4  1 6.2748  32.018 1.569e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 106916.2
## 2     2 106886.2

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge    0.05650    0.09138   0.618    0.536    
## phi   0.02967    0.00544   5.455 5.01e-08 ***
## a    15.08533    1.52106   9.918  < 2e-16 ***
## b   154.85207    6.93604  22.326  < 2e-16 ***
## c   186.83134   15.64827  11.939  < 2e-16 ***
## d     1.58443    0.06894  22.982  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4427 on 10054 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (3 observations deleted due to missingness)

summary

simple model: fits
phi model: fits

plot residuals

predict and plot

plotting 2

M221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1  13158     2159.7                         
## 2  13157     2159.7  1      0       0      1
##   model      AIC
## 1     1 145111.3
## 2     2 145113.3

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge   0.66998    0.07326   9.145   <2e-16 ***
## a   27.60308    1.42684  19.346   <2e-16 ***
## b  127.24722    2.60234  48.897   <2e-16 ***
## c  107.28587    3.05414  35.128   <2e-16 ***
## d    1.35134    0.03717  36.352   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4051 on 13158 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (2 observations deleted due to missingness)

summary

simple model: fits
phi model: fits

plot residuals

predict and plot

plotting 2

M223 - Ozark Broadleaf Forest Meadow

model selection 1

## Error in nls(f_ln_1, data = P_M223, start = c(ge = ge.start, a = a.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
## Error in nls(f_ln_2, data = P_M223, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
##   model AIC
## 1     1  NA
## 2     2  NA

## Warning in min(AIC1_M223$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf

## Error in get(paste("nls_M223.", Mod.Sel1, sep = "")) : 
##   object 'nls_M223.' not found

summary

simple model: does not fit
phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

M231 - Ouachita Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value  Pr(>F)  
## 1   1482     342.11                             
## 2   1481     341.16  1 0.94375  4.0968 0.04314 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 15289.65
## 2     2 15287.55

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge  1.658e-01  2.521e-01   0.658   0.5108    
## phi 3.674e-02  1.853e-02   1.983   0.0475 *  
## a   3.215e+00  4.266e+00   0.754   0.4512    
## b   2.277e+02  1.231e+02   1.850   0.0646 .  
## c   8.349e+02  1.151e+03   0.725   0.4684    
## d   2.737e+00  7.004e-01   3.908 9.72e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.48 on 1481 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96879, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -18.544, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

M242 - Cascade Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df      Sum Sq F value Pr(>F)
## 1   7932       4824                              
## 2   7931       4824  1 -1.0768e-09       0      1
##   model      AIC
## 1     1 105695.1
## 2     2 105697.1

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge 8.961e-03  1.632e-01   0.055    0.956    
## a  0.000e+00  7.564e+00   0.000    1.000    
## b  5.220e+02  4.142e+01  12.603  < 2e-16 ***
## c  8.633e+02  1.940e+02   4.449 8.74e-06 ***
## d  2.514e+00  1.750e-01  14.370  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7799 on 7932 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (3 observations deleted due to missingness)

summary

simple model: fits
phi model: fits ## plot residuals

predict and plot

plotting 2

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

model selection 1

## Warning in log(STDAGE/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model

## Warning in log(STDAGE/c): NaNs produced

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model AIC
## 1     1  NA
## 2     2  NA

## Warning in min(AIC1_M261$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf

## Error in get(paste("nls_M261.", Mod.Sel1, sep = "")) : 
##   object 'nls_M261.' not found

summary

simple model: does not fit
phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot data with prediction"

M262 - California coastal range - coniferous forest - open woodland - shrub meadow

model selection 1

summary

simple model: does not fit
phi model: does not fit

plot residuals

## [1] "cannot plot residuals"

model can fit - but K is negative (only 19 observations) - model excluded

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    907     273.82                          
## 2    906     273.21  1 0.60241  1.9976 0.1579
##   model      AIC
## 1     1 9513.399
## 2     2 9513.390

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge   -0.82619    0.28070  -2.943  0.00333 ** 
## phi   0.02915    0.01893   1.540  0.12387    
## a    25.27188    5.34178   4.731 2.59e-06 ***
## b   111.54653   10.25159  10.881  < 2e-16 ***
## c   150.89398   11.70684  12.889  < 2e-16 ***
## d     0.84635    0.09253   9.147  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5491 on 906 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.94701, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -7.9897, p-value = 1.353e-15
## alternative hypothesis: two.sided

predict and plot

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1   5204     1792.8                           
## 2   5203     1792.8  1 0.000435  0.0013 0.9717
##   model     AIC
## 1     1 54507.6
## 2     2 54509.6

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge  -0.98350    0.09788  -10.05   <2e-16 ***
## a   23.84555    1.53003   15.59   <2e-16 ***
## b  132.20661    6.39948   20.66   <2e-16 ***
## c  257.07744   23.79494   10.80   <2e-16 ***
## d    1.45077    0.08268   17.55   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5869 on 5204 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (27 observations deleted due to missingness)

summary

simple model: fits
phi model: fits

plot residuals

predict and plot

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6770     3131.6                                
## 2   6769     3119.2  1 12.359  26.821 2.297e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 73749.96
## 2     2 73725.17

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge  4.126e-01  1.878e-01   2.197   0.0281 *  
## phi 4.961e-02  8.995e-03   5.516  3.6e-08 ***
## a   1.625e+01  9.543e-01  17.027  < 2e-16 ***
## b   1.072e+02  4.832e+00  22.194  < 2e-16 ***
## c   2.120e+02  1.160e+01  18.278  < 2e-16 ***
## d   1.376e+00  5.654e-02  24.341  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6788 on 6769 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (5 observations deleted due to missingness)

summary

simple model: fits
phi model: fits

plot residuals

predict and plot

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)    
## 1   4432     1818.5                               
## 2   4431     1813.3  1 5.2046  12.718 0.000366 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 49380.46
## 2     2 49369.75

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##      Estimate Std. Error t value Pr(>|t|)    
## ge    0.38596    0.22716   1.699 0.089375 .  
## phi   0.03892    0.01063   3.663 0.000252 ***
## a    18.80827    1.08906  17.270  < 2e-16 ***
## b   130.47290    6.45246  20.221  < 2e-16 ***
## c   137.56631    4.44177  30.971  < 2e-16 ***
## d     1.09670    0.03414  32.122  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6397 on 4431 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (3 observations deleted due to missingness)

summary

simple model: fits
phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93137, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -19.315, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

M334 - Black Hills Coniferous Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    710     277.98                            
## 2    709     276.92  1 1.0638  2.7236 0.09932 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 7186.079
## 2     2 7185.338

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * 
##     (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)
## ge  -3.341e-01  3.837e-01  -0.871    0.384
## phi  3.183e-02  1.948e-02   1.634    0.103
## a    5.701e+00  2.127e+01   0.268    0.789
## b    1.894e+02  5.143e+02   0.368    0.713
## c    5.000e+03  4.717e+04   0.106    0.916
## d    3.745e+00  4.918e+00   0.761    0.447
## 
## Residual standard error: 0.625 on 709 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.95662, p-value = 1.105e-13
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -8.8529, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##   Res.Df Res.Sum Sq Df      Sum Sq F value Pr(>F)
## 1    486     175.73                              
## 2    485     175.73  1 -1.6266e-10       0      1
##   model      AIC
## 1     1 4974.722
## 2     2 4976.722

## 
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -1.3835     0.2579  -5.364 1.26e-07 ***
## a   18.5217     3.1507   5.879 7.70e-09 ***
## b  111.2733    12.4104   8.966  < 2e-16 ***
## c  220.2789    41.6622   5.287 1.88e-07 ***
## d    1.3201     0.1853   7.123 3.83e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6013 on 486 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1 observation deleted due to missingness)

summary

simple model: fits
phi model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.90332, p-value < 2.2e-16
## 
## 
## ------

## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.1527, p-value = 2.567e-07
## alternative hypothesis: two.sided

predict and plot

plotting 2

Fitted parameters

Best / selected models by ecoprovince

Code	Ecoregion	Sel.Mod
211	Northeastern Mixed Forest	2
212	Laurentian Mixed Forest	2
221	Eastern Broadleaf Forest	1
222	Midwest Broadleaf Forest	1
223	Central Interior Broadleaf Forest	1
231	Southeastern Mixed Forest	1
232	Outer Coastal Plain Mixed Forest	2
234	Lower Mississippi Riverine Forest	2
242	Pacific Lowland Mixed Forest	1
251	Prairie Parkland (Temperate)	1
255	Prairie Parkland (Subtropical)	1
261	California Coastal Chaparral Forest and Shrub	NA
262	California Dry Steppe	NA
263	California Coastal Steppe - Mixed Forest and Redwood Forest	1
313	Colorado Plateau Semi-Desert	1
315	Southwest Plateau and Plains Dry Steppe and Shrub	NA
321	Chihuahuan Semi-Desert	NA
322	American Semidesert and Desert	NA
331	Great Plains/Palouse Dry Steppe	1
332	Great Plains Steppe	1
341	Intermountain Semi-Desert and Desert	1
342	Intermountain Semi-Desert	1
411	Everglades	1
M211	Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow	2
M221	Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow	1
M223	Ozark Broadleaf Forest Meadow	NA
M231	Ouachita Mixed Forest	2
M242	Cascade Mixed Forest	1
M261	Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow	NA
M262	California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow	NA
M313	Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow	2
M331	Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow	1
M332	Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow	2
M333	Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow	2
M334	Black Hills Coniferous Forest	2
M341	Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow	1

table by ecoprovince

Code	Ecoregion	region	n.obs	n.plots	ge	ge.2.5	ge.97.5	phi	phi.2.5	phi.97.5	alpha	alpha.2.5	alpha.97.5	a	a.2.5	a.97.5	b	b.2.5	b.97.5	c	c.2.5	c.97.5	d	d.2.5	d.97.5
211	Northeastern Mixed Forest	east	9943	3257	-0.2412335	-0.4497812	-0.0326858	0.0481211	0.0355012	0.0607409	NA	NA	NA	28.841474	26.469998	31.21295	131.42371	122.90701	139.94042	126.03678	115.50692	136.56663	1.1023765	1.0234745	1.1812786
212	Laurentian Mixed Forest	east	30395	11945	0.1140061	-0.0127661	0.2407784	0.0000000	-0.0060365	0.0060365	NA	NA	NA	14.452839	13.671200	15.23448	92.71935	89.28687	96.15183	128.41078	120.45184	136.36973	1.4547033	1.3981993	1.5112073
221	Eastern Broadleaf Forest	east	11294	4269	0.0170145	-0.1298727	0.1639017	NA	NA	NA	NA	NA	NA	21.667151	18.721272	24.61303	174.62875	161.49729	187.76020	154.79638	133.38167	176.21110	1.5019436	1.3859194	1.6179677
222	Midwest Broadleaf Forest	east	7913	3189	-0.1807390	-0.4002087	0.0387307	NA	NA	NA	NA	NA	NA	16.597763	14.350454	18.84507	126.23170	117.37387	135.08952	116.00466	104.32712	127.68219	1.2269038	1.1336515	1.3201562
223	Central Interior Broadleaf Forest	east	13446	4895	-0.0157796	-0.1443065	0.1127474	NA	NA	NA	NA	NA	NA	21.632327	18.790866	24.47379	109.74919	103.93832	115.56005	116.08499	105.40672	126.76326	1.4434940	1.3403324	1.5466556
231	Southeastern Mixed Forest	east	19961	7904	0.6880599	0.5391543	0.8369655	NA	NA	NA	NA	NA	NA	13.360558	12.485458	14.23566	144.78186	136.37174	153.19199	142.55533	123.57446	161.53620	1.8732595	1.7807183	1.9658006
232	Outer Coastal Plain Mixed Forest	east	20919	9046	0.2319657	0.0871922	0.3767392	0.0149078	0.0048896	0.0249261	NA	NA	NA	13.153721	12.107322	14.20012	165.02420	151.89072	178.15769	180.02788	146.42621	213.62954	1.9703357	1.8497826	2.0908888
234	Lower Mississippi Riverine Forest	east	2190	937	-0.1275039	-0.5827497	0.3277420	0.0386612	0.0022919	0.0750306	NA	NA	NA	18.505068	10.787721	26.22242	249.58616	101.43803	397.73429	306.23891	-67.43450	679.91232	1.9773181	1.2749868	2.6796494
242	Pacific Lowland Mixed Forest	pacific	246	172	-0.5603063	-1.5232964	0.4026838	NA	NA	NA	NA	NA	NA	31.031987	-15.709302	77.77328	615.52160	310.16376	920.87944	352.76085	27.05174	678.46997	1.8421147	1.1323308	2.5518985
251	Prairie Parkland (Temperate)	east	2787	1036	-0.3362390	-0.6409707	-0.0315074	NA	NA	NA	NA	NA	NA	27.654337	22.912059	32.39661	103.81353	93.02980	114.59726	101.68632	88.65884	114.71380	1.1117727	0.9668465	1.2566990
255	Prairie Parkland (Subtropical)	pacific	1288	659	-0.5128856	-1.0036203	-0.0221509	NA	NA	NA	NA	NA	NA	14.244225	10.210621	18.27783	83.09090	71.37236	94.80944	69.99751	57.14508	82.84995	1.2098430	1.0119033	1.4077827
261	California Coastal Chaparral Forest and Shrub	pacific	56	34	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
262	California Dry Steppe	pacific	0	0	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
263	California Coastal Steppe - Mixed Forest and Redwood Forest	pacific	430	274	2.0492815	0.3941688	3.7043941	NA	NA	NA	NA	NA	NA	0.000000	-110.170512	110.17051	1000.00000	-1170.07033	3170.07033	5000.00000	-31404.83509	41404.83509	3.4866144	-0.4503236	7.4235524
313	Colorado Plateau Semi-Desert	interior west	508	312	-0.7864222	-1.4838778	-0.0889666	NA	NA	NA	NA	NA	NA	25.473773	16.843973	34.10357	110.39796	87.25140	133.54453	131.74298	122.71833	140.76763	0.6679632	0.5549576	0.7809689
315	Southwest Plateau and Plains Dry Steppe and Shrub	interior west	16	12	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
321	Chihuahuan Semi-Desert	interior west	22	14	-1.1327584	-3.5895544	1.3240377	NA	NA	NA	NA	NA	NA	0.000000	-32.609816	32.60982	256.16145	-966.20947	1478.53238	962.44169	-8993.78918	10918.67255	2.3078160	-2.9293683	7.5450004
322	American Semidesert and Desert	interior west	8	5	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
331	Great Plains/Palouse Dry Steppe	interior west	753	473	-0.3459760	-1.3862004	0.6942484	NA	NA	NA	NA	NA	NA	10.025225	4.966406	15.08404	54.45449	38.73241	70.17658	129.89998	75.05163	184.74833	1.4323237	0.9636546	1.9009929
332	Great Plains Steppe	interior west	324	152	-0.2642535	-1.9235370	1.3950299	NA	NA	NA	NA	NA	NA	24.216351	-6.142070	54.57477	321.73583	-3730.27597	4373.74763	1383.23171	-28960.55405	31727.01747	2.3260724	-6.1508064	10.8029511
341	Intermountain Semi-Desert and Desert	interior west	147	93	1.2043907	-1.5075434	3.9163248	NA	NA	NA	NA	NA	NA	29.351705	11.964479	46.73893	67.94252	31.18450	104.70055	141.86797	113.61703	170.11891	0.6582137	0.3819104	0.9345170
342	Intermountain Semi-Desert	interior west	320	222	0.3773512	-2.0384323	2.7931346	NA	NA	NA	NA	NA	NA	16.848265	6.279003	27.41753	48.34601	22.36602	74.32600	120.41512	96.44070	144.38954	0.8567007	0.5002262	1.2131751
411	Everglades	east	170	86	-1.3900149	-2.5151636	-0.2648662	NA	NA	NA	NA	NA	NA	11.069099	-38.867171	61.00537	934.14418	-12378.18402	14246.47237	5000.00000	-144580.06224	154580.06224	3.0309044	-7.5829445	13.6447533
M211	Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow	east	10063	3398	0.0564998	-0.1226288	0.2356283	0.0296737	0.0190109	0.0403364	NA	NA	NA	15.085331	12.103749	18.06691	154.85207	141.25605	168.44808	186.83134	156.15760	217.50507	1.5844284	1.4492894	1.7195674
M221	Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow	east	13165	4970	0.6699803	0.5263827	0.8135780	NA	NA	NA	NA	NA	NA	27.603081	24.806265	30.39990	127.24722	122.14626	132.34818	107.28587	101.29932	113.27242	1.3513443	1.2784788	1.4242098
M223	Ozark Broadleaf Forest Meadow	east	1248	392	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
M231	Ouachita Mixed Forest	east	1488	574	0.1658361	-0.3286921	0.6603644	0.0367390	0.0003998	0.0730783	NA	NA	NA	3.214899	-5.153137	11.58293	227.73280	-13.78808	469.25369	834.90949	-1423.37455	3093.19353	2.7372552	1.3633988	4.1111115
M242	Cascade Mixed Forest	pacific	7940	4900	0.0089612	-0.3109837	0.3289061	NA	NA	NA	NA	NA	NA	0.000000	-14.826575	14.82658	522.02082	440.82731	603.21433	863.30726	482.94235	1243.67218	2.5141501	2.1711867	2.8571134
M261	Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow	pacific	4575	2761	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
M262	California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow	interior west	54	38	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA
M313	Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow	interior west	913	563	-0.8261935	-1.3770856	-0.2753014	0.0291549	-0.0079966	0.0663063	NA	NA	NA	25.271882	14.788180	35.75558	111.54653	91.42690	131.66616	150.89398	127.91830	173.86967	0.8463537	0.6647606	1.0279467
M331	Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow	interior west	5236	3514	-0.9834959	-1.1753756	-0.7916163	NA	NA	NA	NA	NA	NA	23.845553	20.846057	26.84505	132.20661	119.66093	144.75228	257.07744	210.42936	303.72551	1.4507703	1.2886900	1.6128507
M332	Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow	interior west	6780	4293	0.4125899	0.0444181	0.7807617	0.0496127	0.0319800	0.0672454	NA	NA	NA	16.248841	14.378155	18.11953	107.24863	97.77562	116.72164	212.02048	189.28104	234.75992	1.3761817	1.2653523	1.4870111
M333	Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow	interior west	4440	2838	0.3859621	-0.0593855	0.8313096	0.0389236	0.0180926	0.0597546	NA	NA	NA	18.808270	16.673165	20.94337	130.47290	117.82286	143.12294	137.56631	128.85822	146.27439	1.0967019	1.0297679	1.1636359
M334	Black Hills Coniferous Forest	interior west	716	364	-0.3341002	-1.0873426	0.4191422	0.0318262	-0.0064253	0.0700776	NA	NA	NA	5.701161	-36.067216	47.46954	189.39363	-820.25450	1199.04176	5000.00000	-87612.89848	97612.89848	3.7448342	-5.9114757	13.4011440
M341	Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow	interior west	492	287	-1.3834885	-1.8902300	-0.8767470	NA	NA	NA	NA	NA	NA	18.521694	12.331014	24.71237	111.27327	86.88860	135.65793	220.27885	138.41854	302.13916	1.3200946	0.9559446	1.6842445

plot ge

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I

map #2

plot phi (effect of DeltaPDSI)

plot a coefficient

## Warning: Removed 7 rows containing missing values (geom_point).

plot b coefficient

## Warning: Removed 7 rows containing missing values (geom_point).

plot c coefficient

## Warning: Removed 11 rows containing missing values (geom_point).

plot d coefficient

## Warning: Removed 7 rows containing missing values (geom_point).

Calculations - weighted averages

ge (stand biomass enhancement factor in % 2000-2021)

##          region weighted.ge
## 1     entire US  0.11415431
## 2       pacific  0.01943735
## 3          east  0.18894294
## 4 interior west -0.13979300

phi (effect of DeltaPDSI)

##          region weighted.phi
## 1     entire US  0.010287666
## 2       pacific  0.000000000
## 3          east  0.008045572
## 4 interior west  0.026665510

Calculations - weighted averages subsetted to 15 ecoprovinces

211, 212, 221, 223, 231, 232, 234, 251, M211, M221, M223, M231, M242, M261, M332,

ge

##          region weighted.ge
## 1     entire US 0.202434442
## 2       pacific 0.005731607
## 3          east 0.213926432
## 4 interior west 0.412589912

phi

##          region weighted.phi
## 1     entire US   0.01026246
## 2       pacific   0.00000000
## 3          east   0.00854629
## 4 interior west   0.04961268

FIA - NLS Models: Biomass vs. Stand Age – Log-Normal

JAH

2022-10-25

Background

211 - Northeastern Mixed Forest

model selection 1

summary

plot residuals

predict and plot

plotting 2

212 - Laurentian Mixed Forest

model selection 1

summary

plot residuals

predict and plot

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

summary

plot residuals

predict and plot

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

summary

plot residuals

predict and plot

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

summary

plot residuals

predict and plot

plotting 2

231 - Southeastern Mixed Forest

model selection 1

summary

plot residuals

predict and plot

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

summary

plot residuals

predict and plot

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

summary

plot residuals

predict and plot

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

summary

plot residuals

predict and plot

plotting 2

251 - Prairie Parkland (Temperate)

model selection 1

summary

plot residuals

predict and plot

plotting 2

255 - Prairie Parkland (Subtropical)

model selection 1

summary

plot residuals

predict and plot

plotting 2

261 - California Coastal Chaparral Forest and Shrub

model selection 1

summary

plot residuals

predict and plot

plotting 2

262 - California Dry Steppe

model selection 1

summary

plot residuals